So-called fuel cut has conventionally been executed that achieves improvement of fuel efficiency by temporarily stopping fuel injection to an engine during deceleration running of a vehicle. For example, one example is an engine fuel supply control device of Patent Document 1. In the technique disclosed in Patent Document 1, if a condition for stopping fuel injection is satisfied in a vehicle including a manual transmission (manual transmission) at the time of shift of the manual transmission, the fuel injection is not immediately stopped after the satisfaction of the condition, and a predetermined delay time is set so as to stop the fuel injection after waiting for the delay time to pass and, particularly, the delay time is set shorter at the time of upshift as compared to the time of downshift. If the delay time is set as described above, since the fuel injection is promptly stopped at the time of upshift and an engine rotation speed is quickly reduced, the engine rotation speed is rapidly adjusted at the time of upshift and a shift can promptly be achieved. Since the fuel injection is continued at the time of downshift as compared to the time of upshift, a reduction of the engine rotation speed is suppressed and, therefore, the engine rotation speed is rapidly adjusted at the time of downshift and a shift can promptly be achieved.